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In D. P. Sheehan (ed.), Frontiers of Time (Melville, NY: AIP Conference Proceedings), pp. 75-88.

A new event is defined as an intervention in the time reversible dynamical trajectories of particles in a system. New events are then assumed to be quantum fluctuations in the spatial and momentum coordinates, and mental action is assumed to work by ordering such fluctuations. It is shown that when the cumulative values of such fluctuations in a mean free path of a molecule are magnified by molecular interaction at the end of that path, the momentum of a molecule can be changed from its original direction to any other direction. In this way mental action can produce effects through the ordering of thermal motions. Examples are given which show that the ordering of 104-105 molecules is sufficient to (a) produce detectible PK results and (b) open sufficient ion channels in the brain to initiate a physical action. The relationship of the above model to the arrow of time is discussed.

It is shown that if mental influence can change a position or momentum coordinate within the limits of the uncertainty principle, such change, when magnified by a single interaction, is sufficient to order the direction of traveling molecules. Mental influence could initiate an action potential in the brain through this process by using the impact of ordered molecules to open the gates of sodium channels in neuronal membranes. It is shown that about 80 ordered molecules, traveling at thermal velocity in the intercellular medium in the brain, can break an ionic or covalent bond, and that the number needed to initiate an action potential is relatively small. If mental influence can act within the brain, it is reasonable to suppose it can act to some extent outside of it. If mental influence could not only order the direction of individual molecules, but coordinate this effect to produce a longitudinal pressure wave which is reasonably coherent across a macroscopic surface, only 10⁴ molecules need be simultaneously affected to produce a detectible sound wave. Such an effect is not ordinarily observed, which suggests that if mental influence acts by ordering the direction of molecules, it acts at the level of individual molecules, but does not coordinate their motion.

A quantitative theory of the effects of mental influence outside the body, based on the idea that such influence consists of the ordering of random fluctuations within the limits of the uncertainty principle, is used to predict the effects of ordered air molecules on a tumbling cube. If the influence can act throughout the first tumble of a cube, the pressure necessary to produce the deviation effects achieved by Forwald (1959, 1969) is estimated to be 1.45 x 10^-5 dyne/cm2. The number of molecules which must be simultaneously influenced to produce this pressure is 2.41 x 10⁵. The trajectory of a tumbling cube must have a minimum number of steps s₀ in order for any substantial amount of magnification of a change in its trajectory to occur. (A step is a tumble from one corner to another.) When mental effects are produced by ordered molecules, s₀ depends logarithmically on cube parameters (mass, length of a side, velocity), the pressure of the surrounding gas, and the number of molecules a person can simultaneously influence. If a cube of mass M and half-length b is compared to a cube with mass M1 and half-length b1, and all other parameters are constant, then s₀(M,b) - s₀(M1,b1) = log₂(Mb12/M1b2). If different numbers of cubes n and n1 are influenced, with all other parameters constant, then s₀(n) - s₀(n1) = log₂(n/n₁). If values for s0 are compared at pressures P and P₁, with all other parameters constant, then s₀(P) - s₀(P₁) = log₂(P₁/P).

The root mean square perturbations on particles produced by vacuum radiation must be limited by the uncertainty principle, i.e., <dx²>^? <dp_x²>^? = h/2, where <dx²>^? and <dp_x²>^? are the root mean square values of drift in spatial and momentum coordinates. The value <dx²>^? = (ht/m)^?, where m is the mass of the particle, can be obtained both from classical SED calculation and the stochastic interpretation of quantum mechanics. Substituting the latter result into the uncertainty principle yields a fractional change in momentum coordinate, <dp_x²>^? / p, where p is the total momentum, equal to 2^-3/2 (h/Et)^?, where E is the kinetic energy. It is shown that when an initial change <dp_x²>^? is amplified by the lever arm of a molecular interaction, <dp_x²>^? / p > = 1 in only a few collision times. Therefore the momentum distribution of a collection of interacting particles is randomized in that time, and the action of vacuum radiation on matter can account for entropy increase in thermodynamic systems. The interaction of vacuum radiation with matter is time-reversible. Therefore whether entropy increase in thermodynamic systems is ultimately associated with an arrow of time depends on whether vacuum photons are created in a time-reversible or irreversible process. Either scenario appears to be consistent with quantum mechanics.

It is shown that a very small change in the initial angle of orientation of a tumbling cube can be detected by a shift in the endpoint of the trajectory after the cube travels a minimum distance. Specifically, if a cube travels forward in the x direction, with s the number of forward steps (tumbles) in the trajectory, the average sideways deviation DY in final position produced by a change in initial angle 0 dq is given by DY = a(s ? s₀), where a is the average length of the sideways step during each tumble and s₀ a term which depends logarithmically on 0 dq . It is proposed that the reason cubes (dice) are popular in games of chance is because this ability of the cube trajectory to magnify small changes allows the possibility for mental influence to act. A general outline is given for experiments using traveling cubes which can test for the action of mental influence.

The concept of free will is central to our lives, as we make day-to-day decisions, and to our culture, in our ethical and legal systems. The very concept implies that what we choose can produce a change in our physical environment, whether by pressing a switch to turn out electric lights or choosing a long-term plan of action which can affect many people. Yet volition is not a part of presently known physical laws, and it is not even known whether it exists -- no physics experiments have ever established its presence. (We will use the terms volition and free will synonymously in this article.) The purpose of this article is to make two points: first, that free will cannot be accounted for by presently known physical laws, and second, that if free will exists, any description of its effects in the physical world necessarily would constitute a radical addition to presently known physical laws...